Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6633)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=1, a₃>=1

For fixed z and a₁=-7/2, a₂=1, a₃=1

For fixed z and a₁=-7/2, a₂=1, a₃=1, b₁=-5/2

http://functions.wolfram.com/07.27.03.6633.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 1}, {-(5/2), -(1/2)}, -z] == (480 + 1824 z - 5096 z^2 + 34300 z^3 + 11025 Pi^2 z^(7/2) + 44100 z^4 + 11025 Pi^2 z^(9/2))/(480 (1 + z)) + (1/(245760 (1 + z)^(17/2))) ((-245760 - 3102168 z - 8885868 z^2 - 40823480 z^3 - 356732375 z^4 - 1935472935 z^5 - 5364285983 z^6 - 9144827153 z^7 - 10119651150 z^8 - 7338344160 z^9 - 3380045760 z^10 - 900103680 z^11 - 105799680 z^12) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(245760 (1 + z)^(17/2))) ((245760 + 3102168 z + 8885868 z^2 + 40823480 z^3 + 356732375 z^4 + 1935472935 z^5 + 5364285983 z^6 + 9144827153 z^7 + 10119651150 z^8 + 7338344160 z^9 + 3380045760 z^10 + 900103680 z^11 + 105799680 z^12) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (7 (-6 z^(3/2) + 21 z^(5/2) + 140 z^(7/2) + 105 z^(9/2)) Log[Sqrt[z] + Sqrt[1 + z]])/(8 (1 + z)^(3/2)) + (1/(245760 (1 + z)^(17/2))) ((245760 + 3102168 z + 8885868 z^2 + 40823480 z^3 + 356732375 z^4 + 1935472935 z^5 + 5364285983 z^6 + 9144827153 z^7 + 10119651150 z^8 + 7338344160 z^9 + 3380045760 z^10 + 900103680 z^11 + 105799680 z^12) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) + (735/8) z^(7/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])] + (735/8) z^(7/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (735/8) z^(7/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]

Standard Form

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MathML Form

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<msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40823480 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8885868 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3102168 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 245760 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 105 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 140 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]