Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.2679)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=1, b_1`>=-11/2

For fixed z and a₁=1, b₁=-11/2

http://functions.wolfram.com/07.22.03.2679.01

Input Form

HypergeometricPFQ[{1}, {-(11/2), 6}, z] == (1/(2772 z^5)) (45045 (305235 - 29070 z + 1530 z^2 - 60 z^3 + 2 z^4) - 33 (416645775 + 793611000 z + 200491200 z^2 + 14676480 z^3 + 349440 z^4 + 2048 z^5) Cosh[2 Sqrt[z]] + 2 Sqrt[z] (13749310575 + 7856748900 z + 1029188160 z^2 + 43243200 z^3 + 549120 z^4 + 1024 z^5) Sinh[2 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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]