Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8907)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8907.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(23/4)}, -z] == (Sqrt[2] ((20635351038225 + 28674829854720 z - 8649356567040 z^2 + 944880943104 z^3 - 53302394880 z^4 + 1761607680 z^5 - 33554432 z^6) BesselJ[1/4, Sqrt[z]]^2 + 96 Sqrt[z] (-596291546025 + 149512282920 z - 15536586240 z^2 + 857708544 z^3 - 27983872 z^4 + 524288 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-31621769668125 + 36308196086400 z - 9416606814720 z^2 + 986692976640 z^3 - 54656630784 z^4 + 1786773504 z^5 - 33554432 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(20635351038225 z^(1/4))

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]