Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7389)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-23/4

http://functions.wolfram.com/07.22.03.7389.01

Input Form

HypergeometricPFQ[{5}, {-(23/4), 23/4}, -z] == (1/(36175872 z^(19/4))) (-12 z^(3/4) (5293484571375 - 1546033589100 z + 202897094400 z^2 - 14936201280 z^3 + 718658816 z^4 - 24038400 z^5 + 376832 z^6) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-47641361142375 + 32063392260900 z - 6561074520000 z^2 + 650490160320 z^3 - 38711312640 z^4 + 1583662080 z^5 - 40992768 z^6 + 262144 z^7) Cos[2 Sqrt[z]] + (47641361142375 - 95585207117400 z + 32373113572800 z^2 - 4451282035200 z^3 + 334979124480 z^4 - 16328632320 z^5 + 554631168 z^6 - 8912896 z^7) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-47641361142375 + 95585207117400 z - 32373113572800 z^2 + 4451282035200 z^3 - 334979124480 z^4 + 16328632320 z^5 - 554631168 z^6 + 8912896 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-47641361142375 + 32063392260900 z - 6561074520000 z^2 + 650490160320 z^3 - 38711312640 z^4 + 1583662080 z^5 - 40992768 z^6 + 262144 z^7) Sin[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]