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

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=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(11/2), 1/2}, -z] == (1/155925) (155925 + 510300 z + 661500 z^2 + 705600 z^3 + 816480 z^4 + 1330560 z^5 + 5765760 z^6 - 6428655 z^7 + 2263635 z^8 - 362824 z^9 + 28896 z^10 - 1104 z^11 + 16 z^12) + (1/311850) ((Sqrt[Pi] (-16380945 z^(13/2) + 14820855 z^(15/2) - 4863810 z^(17/2) + 753480 z^(19/2) - 58880 z^(21/2) + 2224 z^(23/2) - 32 z^(25/2)) Erfi[Sqrt[z]])/E^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]