Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1275)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=5/2

http://functions.wolfram.com/07.22.03.1275.01

Input Form

HypergeometricPFQ[{-(7/2)}, {5/2, 4}, z] == (1/(28828800 z^(5/2))) (4 (2 Sqrt[z] (-100800 + 604800 z + 5949825 z^2 - 5600320 z^3 + 808032 z^4 - 29184 z^5 + 256 z^6) BesselI[0, 2 Sqrt[z]] + (201600 - 1108800 z - 3737475 z^2 + 5220680 z^3 - 793664 z^4 + 29056 z^5 - 256 z^6) BesselI[1, 2 Sqrt[z]]) - Pi z^(3/2) (4729725 + 18918900 z - 21621600 z^2 + 3203200 z^3 - 116480 z^4 + 1024 z^5) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(3/2) (4729725 + 18918900 z - 21621600 z^2 + 3203200 z^3 - 116480 z^4 + 1024 z^5) BesselI[0, 2 Sqrt[z]] StruveL[1, 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]