Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0518)

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=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=1/2

http://functions.wolfram.com/07.22.03.0518.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1/2, 9/2}, -z] == (1/(212336640 z^(7/2))) (2 Sqrt[z] (-7016625 - 3742200 z - 6548850 z^2 + 60228360 z^3 + 49283730 z^4 + 6848640 z^5 + 283164 z^6 + 3952 z^7 + 16 z^8) Cos[2 Sqrt[z]] + (7016625 - 5613300 z - 935550 z^2 + 34927200 z^3 + 43761870 z^4 + 6586200 z^5 + 279300 z^6 + 3936 z^7 + 16 z^8) Sin[2 Sqrt[z]] + 32 z^4 (9823275 + 6548850 z + 873180 z^2 + 35640 z^3 + 495 z^4 + 2 z^5) SinIntegral[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]