Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a9r1)

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=3, b₁=11/2

http://functions.wolfram.com/07.25.03.a9r1.01

Input Form

HypergeometricPFQ[{-(3/2), 3}, {11/2, 6}, -z] == -((60 (36 + 234 z + 143 z^2))/(143 z^5)) + (5 (221184 + 712935 z + 174630 z^2 - 23352 z^3 + 8592 z^4 + 3632 z^5 + 224 z^6))/(E^z (73216 z^5)) + (1/(146432 z^(9/2))) (5 Sqrt[Pi] (945945 + 1621620 z + 324324 z^2 - 41184 z^3 + 20592 z^4 + 7488 z^5 + 448 z^6) 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]