Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ant2)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-7/2

http://functions.wolfram.com/07.25.03.ant2.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(7/2), -(3/2)}, z] == (1/4465125) (4465125 + 28066500 z + 510810300 z^2 - 13621608000 z^3 + 347351004000 z^4 + 3268407542400 z^5 + 7230113654400 z^6 + 6852813891840 z^7 + 3427897190400 z^8 + 1004809680000 z^9 + 182917365120 z^10 + 21318136560 z^11 + 1605522864 z^12 + 77201280 z^13 + 2273280 z^14 + 37120 z^15 + 256 z^16) + (1/4465125) (8 E^z Sqrt[Pi] (125707982400 z^(9/2) + 674251905600 z^(11/2) + 1208950369200 z^(13/2) + 1027714035600 z^(15/2) + 482438640600 z^(17/2) + 135913097880 z^(19/2) + 24107555745 z^(21/2) + 2760621615 z^(23/2) + 205379010 z^(25/2) + 9789960 z^(27/2) + 286464 z^(29/2) + 4656 z^(31/2) + 32 z^(33/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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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,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]