Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ahy6)

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=3, a₃>=3

For fixed z and a₁=-3/2, a₂=3, a₃=3

For fixed z and a₁=-3/2, a₂=3, a₃=3, b₁=-1/2

http://functions.wolfram.com/07.27.03.ahy6.01

Input Form

HypergeometricPFQ[{-(3/2), 3, 3}, {-(1/2), 7/2}, -z] == -((5 (1728 + 1824 z - 5096 z^2 + 34300 z^3 + 11025 Pi^2 z^(7/2) + 44100 z^4 + 11025 Pi^2 z^(9/2)))/(32768 z^2 (1 + z))) + (1/(65536 (1 + z)^(17/2))) (5 (512 + 2025216 z - 11083208 z^2 + 33469688 z^3 + 67550400 z^4 + 116523202 z^5 + 129389361 z^6 + 94053117 z^7 + 43397433 z^8 + 11571705 z^9 + 1361430 z^10) Log[1 + Sqrt[z] - Sqrt[1 + z]]) - (1/(65536 (1 + z)^(17/2))) (5 (512 + 2025216 z - 11083208 z^2 + 33469688 z^3 + 67550400 z^4 + 116523202 z^5 + 129389361 z^6 + 94053117 z^7 + 43397433 z^8 + 11571705 z^9 + 1361430 z^10) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (15 (-144 - 248 z - 210 z^2 + 735 z^3 + 4900 z^4 + 3675 z^5) Log[Sqrt[z] + Sqrt[1 + z]])/(8192 z^(5/2) (1 + z)^(3/2)) - (1/(65536 (1 + z)^(17/2))) (5 (512 + 2025216 z - 11083208 z^2 + 33469688 z^3 + 67550400 z^4 + 116523202 z^5 + 129389361 z^6 + 94053117 z^7 + 43397433 z^8 + 11571705 z^9 + 1361430 z^10) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) - (55125 z^(3/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/8192 - (55125 z^(3/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/8192 + (55125 z^(3/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/8192

Standard Form

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MathML Form

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</mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 11025 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 44100 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11025 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 34300 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5096 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1824 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1728 </mn> </mrow> <mo> ) </mo> </mrow> 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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]